Stiffness of cloth jacket
By material, I assume you mean the mesh. For the purpose of simulating the cloth, the answer is no you don't need volume/thickness.

You can dynamically add thickness that is not calculated in the simulation by adding a Solidify modifier after the cloth modifier. This may be useful if you want the cloth mesh to appear thicker without slowing down the simulation
AFAIK, no. I have seen no visible differences after running a few tests.
I'm not sure what you mean. Could you try and explain more/add screenshots?

From the wiki: 


  Structural
  Overall stiffness of the cloth. 
  
  Bending
  Wrinkle coefficient. Higher creates more large folds. 



Also see the wiki page on cloth simulation.